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Extra resources for Calculus: A Complete Course (7th Edition)
41. 42. y = x 2 + 3, y = 3x + 1 y = x2 y = 4x 6, x 2 + y 2 = 25, 2x 2 + 2y 2 = 5, x2 3x + 4y = 0 xy = 1 In Exercises 43 50, identify and sketch the curve represented by the given equation. (3, 3) Version (b) 45. x 4 Version (d) (4, 2) Version (a) 3 47. x2 + y2 = 1 4 3)2 (x 9 x2 4 + 44. 9x 2 + 16y 2 = 144 (y + 2)2 = 1 46. (x 4 y2 = 1 48. x 2 1)2 + y2 = (y + 1)2 =4 4 1 49. x y = 4 50. (x 1)(y + 2) = 1 51. What is the effect on the graph of an equation in x and y of (a) replacing x with x? (b) replacing y with y?
G(x) 1)/2) (1, 1) In Exercises 8 10, construct the following composite functions and specify the domain of each. (a) f f (x) (b) f g(x) (c) g f (x) (d) g g(x) f (x) (1/2) f (x) x 5. x + |x| 6. |x| + |x 2| 7. 65. Sketch the graphs of the indicated functions, and specify their domains and ranges. 2x, 1 1 2x 1. x x if x 0 if x < 0. Why is f (x) called the integer part of x? 6: Polynomials and Rational Functions * Even and odd functions 33. Assume that f is an even function, g is an odd function, and (a) Show that f is the sum of an even function and an odd function: both f and g are de ned on the whole real line .
For what value of k are the lines parallel? 50. Find the line that passes through the point (1, 2) and through the point of intersection of the two lines x + 2y = 3 and 2x 3y = 1. Graphs of Quadratic Equations This section reviews circles, parabolas, ellipses, and hyperbolas, the graphs that are represented by quadratic equations in two variables. Circles and Disks The circle having centre C and radius a is the set of all points in the plane that are at distance a from the point C. + The distance from P(x , y) to the point C(h, k) is (x h)2 + (y k)2 , so that 18 PRELIMINARIES the equation of the circle of radius a > 0 with centre at C(h, k) is * (x h)2 + (y k)2 = a.